Alvarus, Thomas
,
Liber de triplici motu
,
1509
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Tertii tractatus
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203
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<
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xml:space
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">Secundū capitulū huiꝰ tractatus / in quo ſolito
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pro more diſputatiue inquirimus penes quid velo
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citas augmētationis attendi habeat.</
head
>
<
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<
s
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xml:space
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">NUnc cõſequēter q̄ritur vtrū
<
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velocitas motus augmētatiõis penes ꝓ
<
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portionalē acquiſitionē ̄titatis attēdi
<
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habeat: an penes abſolutã acq̇ſitione ̄titatis.</
s
>
</
p
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<
p
xml:id
="
N24026
">
<
s
xml:id
="
N24027
"
xml:space
="
preserve
">Arguitur primo / non penes propor
<
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tionabilē acquiſitionē ̄titatis ita non ſemꝑ illḋ
<
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/>
quod in eodē tꝑe maiorem ꝓportionē acquirit ̄
<
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/>
aliud velocius augmētetur ꝙ̄ aliud in eodē tēpore
<
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/>
quia ſi ſic tūc ſequeretur / a. et b. ſunt equalia: et a
<
lb
/>
continuo velocius augmētabit̄̄ ꝙ̄ b. et tamen ſemꝑ
<
lb
/>
a. manebit minus .b. / ſꝫ conſequēs eſt manifeſte fal-
<
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/>
ſum: igitur illud ex quo ſequit̄̄. </
s
>
<
s
xml:id
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N24038
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xml:space
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preserve
">Sequela ꝓbat̄̄: et
<
lb
/>
volo / .a. et .b. ſint duo pedalia: et acquirat vnifor-
<
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/>
miter .b. in hora vnū pedale: et nichil deperdat de
<
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/>
qnantitate prehabita .a vero acquirat vnū pedale
<
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/>
vniformiter ꝑ horã: et deꝑdat vnū ſemipedale ̄ti-
<
lb
/>
tatis prehabite vniformiter in illa hora. </
s
>
<
s
xml:id
="
N24045
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xml:space
="
preserve
">quo poſi-
<
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/>
to arguitur ſic / .a. et .b. ſunt modo equalia: et ſemꝑ .a
<
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/>
poſt hoc manebit minꝰ .b. / vt cõſtat qm̄ ſi nichil de
<
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/>
perderet maneret equale: ſꝫ modo cõtinuo perdet.
<
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/>
</
s
>
<
s
xml:id
="
N2404F
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xml:space
="
preserve
">ergo cõtinuo manet minus: et tamē .a. cõtinuo velo
<
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/>
cius augmētabitur ꝙ̄ .b. / igitur intentū. </
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>
<
s
xml:id
="
N24054
"
xml:space
="
preserve
">Probatur
<
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/>
minor / q2 .a. cõtinuo erit minus .b. et cõtinuo equa-
<
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lem ̄titatē acquiret cū .b. / igit̄̄ .a. cõtinuo maiorem
<
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/>
ꝓportionē acquiret ꝙ̄ .b. et penes acq̇ſitionē maio
<
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/>
ioris ꝓportiõis in eodē tēpore attēdit̄̄ maior veloci
<
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/>
tas augmētatõis: igit̄̄ .a. ↄ̨tinuo velociꝰ augmētabi
<
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/>
tur ꝙ̄ .b. / quod fuit ꝓbandū. </
s
>
<
s
xml:id
="
N24063
"
xml:space
="
preserve
">Hec ↄ̨ſequētia patꝫ de
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ſe: et prior ex octaua ſuppoſitiõe quarti capitis ſe-
<
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/>
cunde partis: et in aliis pleriſ locis libri arguta
<
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/>
eſt.
<
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xml:space
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">Dicitur</
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<
s
xml:id
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N24071
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xml:space
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">¶ Dices et bene negando ſequelam: et ad ꝓbatio
<
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/>
nē admiſſo caſu ad bonū ſenſum poſſet em̄ negari /
<
lb
/>
vt poſtea dicemus: reſpõdeo negando minorē vi-
<
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/>
delicet / .a. cõtinuo poſt hoc velocius augmentabi
<
lb
/>
tur ꝙ̄ .b. et ad ꝓbationē concedo / .a. cõtinuo mane
<
lb
/>
bit minus et nego / ↄ̨tinuo equalē quãtitatem acq̇
<
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/>
ret cū .b. ſicut de facto eſt negandū qm̄ ſi nichil de-
<
lb
/>
perderet ſemꝑ acquireret equalē ̄titatē: ſꝫ modo
<
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/>
cõtinuo deꝑdit: ergo cõtinuo acquirit minorē: quo
<
lb
/>
niã in tota hora nõ acquirit .a. niſi ſemipedale. </
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<
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xml:space
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">Ma
<
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nebit em̄ in fine pedale cū dimidio quoniã mãſiſſet
<
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/>
bipedale niſi perdidiſſet dimidiū. </
s
>
<
s
xml:id
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N2408D
"
xml:space
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preserve
">¶ Item in inſtã-
<
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/>
ti medio hore acquiſiuit .a. vnã quartã pedalis .b.
<
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/>
vero vnã medietatē: et ſic in illa prīa medietate ma
<
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/>
iorē quãtitatē acquiſiuit .b. ꝙ̄ .a. cuius oppoſitum
<
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/>
aſſumit argumētum.
<
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xml:space
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<
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ca'lcna.</
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>
</
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<
s
xml:id
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xml:space
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">¶ Ex quo a ꝑte infertur cal-
<
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latorē male induxiſſe illud cõſequēs tan̄ ſequens
<
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ex opinione quam impugnamus: qm̄ illa cõcluſio
<
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nullo pacto ſequit̄̄ expoſitione. </
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>
<
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xml:space
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">Teneat̄̄ igit̄̄ poſi-
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tio vniuerſaliter.</
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</
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<
s
xml:id
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xml:space
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">Sed contra hanc reſponſionē argui
<
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tur ſic / quia ſi illa poſitio eſſet vniuerſaliter vera / ſe
<
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/>
queretur hec concluſio. </
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>
<
s
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xml:space
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preserve
"> ſi ſint duo ſiue equalia ſiue
<
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inequalia q̄ cõtinuo eque velociter diminuãtur per
<
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dendo cõtinuo equales ꝓportiones eque cito veni-
<
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/>
ent ad non quãtum: ſed ↄ̨ſequens eſt falſum: igitur
<
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/>
illud ex quo ſequit̄̄: falſitas ↄ̨ſequētis ꝓbat̄̄: q2 ſtat
<
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/>
aliqua duo in aliquo tepore eque velociter dimi
<
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/>
nuatur ꝑdendo in illo tꝑe p̄ciſe .4. duplas: igit̄̄ tūc
<
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/>
ↄ̨tinuo eque velociter diminuētur: et tamē nõ eque
<
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/>
cito deueniēt ad nõ ̄tū: et ꝑ ↄ̨ſequēs illḋ illatuꝫ eſt
<
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/>
vna conditionalis q̄ eſt falſa: igitur illud cõſequēs
<
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eſt falſum. </
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>
<
s
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N240DC
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xml:space
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">¶ Dices et bñ / de rigore illud ↄ̨ſequēs
<
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eſt falſum ̄uis ſub illa forma ponatur a calcula-
<
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/>
tore: ſed oportet addere in antecedende illius con-
<
cb
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Capi. ſecundum
"/>
ditionalis q̄ eque velociter diminuūtur vſ ad nõ
<
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/>
quãtū: et tūc illa ↄ̨cluſio eſt ↄ̨cedenda ſecundū opi-
<
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nionē. </
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>
<
s
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xml:space
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">Quod ſic oſtēditur / quoniã ſi aliquod corpꝰ
<
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puta .a. in hora diminuat̄̄ ad nõ quãtū: illud corpꝰ
<
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infinitã latitudinē ꝓportionū deperdet: et .b. aliud
<
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corpus maius in tota illa hora eque velociter di-
<
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/>
minuitur cū .a. / ergo ſequit̄̄ / infinitã latitudinē ꝓ-
<
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portionis etiã deperdit .b. in illa hora: et vltra infi
<
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nitã latitudinē ꝓportionis deperdit .b. in illa hora
<
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et nõ reſtituit̄̄ in inſtanti terminatiuo priſtine quã
<
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titati vt volo: igit̄̄ in inſtãti termīatiuo hore .b. erit
<
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nõ ̄tum: et tunc .a. erit nõ ̄tum: igitur eq̄ cito .a. et .b.
<
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deuenient ad nõ ̄tū in tali caſu: qḋ fuit ꝓbandum
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</
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>
<
s
xml:id
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N24102
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xml:space
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">Sꝫ tã probo hanc cõſequētiã .b. inifinitã latitudinē
<
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ꝓportiõis deꝑdit ī hora et ñ reſtituit̄̄ in inſtanti ter
<
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minatiuo priſtine ̄titati: ergo in illo inſtanti non
<
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quãtū manet </
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>
<
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xml:space
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">Quia ſi in illo inſtãti maneret alicuiꝰ
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quãtitatis: ſit illa quãtitas vna milleſima exempli
<
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gratia: et tã ſequit̄̄ / in illa hora nõ deꝑdit niſi mil
<
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/>
lecuplã ꝓportionē: et per ↄ̨ſequēs nõ infinitã / quod
<
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eſt oppoſitū ↄ̨ſequētis. </
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>
<
s
xml:id
="
N24116
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xml:space
="
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">Et iſto modo ꝓbat̄̄ hec ↄ̨ſe-
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quētia prius facta deuenit .a. ad nõ ̄tum / ergo infi
<
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nitam ꝓportionē deperdit: quia ſi ſolū finita puta
<
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millecuplã iam illud in fine maneret vt vna milleſi
<
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ma et ſic non maneret nõ quãtum.</
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>
</
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>
<
p
xml:id
="
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<
s
xml:id
="
N24122
"
xml:space
="
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">Sed contra hoc arguitur ſic / quia ſi
<
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/>
hoc eſſet verū ſeq̇retur eodē mõ / ſi in aliqua duo
<
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/>
ſiue equalia ſiue inequalia in certa ꝓportione cõti
<
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/>
nuo inequaliter diminuãtur vſ ad non quãtum ta
<
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/>
lia eque cito deueniunt ad nõ quãtū: ſed conſequēs
<
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videtur falſum: igitur illud ex quo ſequitur. </
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>
<
s
xml:id
="
N2412F
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xml:space
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">Seq̄la
<
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ꝓbatur et volo / ſint .a. et .b. pedale: et ꝑdat .a. in
<
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qualibet parte ꝓportionali ꝓportionē quadruplã
<
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b. vero ſemꝑ in duplo minorē proportionē in qua
<
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libet parte ꝓportionali puta ꝓportionē duplam.
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/>
</
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<
s
xml:id
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N2413B
"
xml:space
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">Et arguitur ſic / cū primū .a. ꝑdiderit infinitas ꝓpor
<
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tiones quadruplas ip̄m deuenerit ad non quantū:
<
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/>
et tunc .b. ꝑdidit īfinitas duplas / vt patet ex caſu: er
<
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go tunc .b. deuenit ad nõ quãtū. </
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>
<
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xml:id
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N24144
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xml:space
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">Nõ em̄ poteſt infini
<
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tas duplas perdere quī infinitã latitudinē ꝓportio
<
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nis deperdat: et ꝑ conſequens eque cito .a et .b. de-
<
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uenient ad nõ quãtū: quod fuit probandū. </
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>
<
s
xml:id
="
N2414D
"
xml:space
="
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">Et iſto
<
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modo probabis de q̇buſcū aliis corporibus ſiue
<
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equalibus ſiue inequalibus: dūmodo vnum altero
<
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/>
in certa ꝓportione continuo velocius diminuatur
<
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ad non quantum.</
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>
</
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>
<
p
xml:id
="
N24158
">
<
s
xml:id
="
N24159
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xml:space
="
preserve
">Secūdo prīcipaliter ad idem arguit̄̄
<
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ſic. </
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>
<
s
xml:id
="
N2415E
"
xml:space
="
preserve
">Si velocitas augmētatiõis attenderet̄̄ penes ꝓ
<
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portionalē acquiſitionē quãtitatis: ſequeretur hec
<
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/>
concluſio / ſi aliquid inciperet ſucceſſiue augeri
<
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/>
a non quãto: ipſum infinite velociter inciperet au-
<
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/>
geri: ſꝫ conſequens eſt falſum: igitur illud ex quo ſe
<
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/>
quitur. </
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>
<
s
xml:id
="
N2416B
"
xml:space
="
preserve
">Falſitas cõſequēs arguit̄̄ ſic: q2 tunc ſeq̇re
<
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tur / quodlibet tale infinite velociter inciperet ac-
<
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quirere de quãtitate: ſꝫ ↄ̨ſequens eſt falſum: igitur
<
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/>
illud ex quo ſequitur. </
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>
<
s
xml:id
="
N24174
"
xml:space
="
preserve
">Sed tã probo ſequelam / quia
<
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ſi .a. incipit augeri a nõ quãto poſt inſtans inceptio
<
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/>
nis talis augmentationis ipſum eſt aliquãtum: et
<
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/>
ante illud inſtans fuit in duplo minus: et in triplo
<
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/>
et in quadruplo et ſic infinitum: ergo inter illud in
<
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/>
ſtans et īſtans initiatiuū illud acquiſiuit infinitam
<
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/>
proportionem: et per cõſequēs ſequit̄̄ / ipſum infi-
<
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/>
nite velociter incipit augeri. </
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>
<
s
xml:id
="
N24185
"
xml:space
="
preserve
">patet conſequentia ex
<
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poſitione.
<
note
position
="
right
"
xlink:href
="
note-0203-03a
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xlink:label
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note-0203-03
"
xml:id
="
N241A8
"
xml:space
="
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">Dictur.</
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>
</
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>
<
s
xml:id
="
N2418F
"
xml:space
="
preserve
">¶ Dices et bene concedendo cõcluſioneꝫ
<
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/>
illatam / vt bene ꝓbat argumentū / et negando falſi
<
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/>
tatem conſequentis: et ad probationē nego iſtam
<
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/>
conſequentiã infinite velociter incipit augeri: ergo
<
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/>
infinite velociter incipit a. acquirerere de quãtitate / </
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>
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>
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